The star architecture of the multiple access communications system consists of a hub station in the center of the star and remote stations of which there is one each at the points of the star. It is assumed that a communications path exists by which the hub station transmits information to each of the remote stations and this path is called the Forward Link. It is assumed that a communications path exists by which an individual remote station transmits information to the hub station and this path is called the Return Link. A star architecture with K remote stations is shown in FIG. 1.
The object of this invention is to provide a method for synchronizing the code sequences of subscribers in a Doubly Orthogonal Code and Frequency Division Multiple Access (DOCDMA) communications system.
This invention is applicable to a DOCDMA communications system which is configured in a star architecture. The DOCDMA system is described in U.S. patent application Ser. No. 444,749, filed May 19, 1995, entitled DOUBLY ORTHOGONAL CODE AND FREQUENCY DIVISION MULTIPLE ACCESS COMMUNICATION SYSTEM, also incorporated herein by reference. In this system, multiple OCDMA signals are transmitted on orthogonally spaced carriers such that a single remote station transmits on a single orthogonal function on a single carrier frequency. FIG. 2 illustrates the composite frequency spectrum for DOCDMA signals. It is necessary in this application that all Return Link signals received at the hub station are time synchronous. The signals possess the same Time Division Multiplex structure in which a portion of the signal is dedicated to a time synchronization burst. This invention specifies that synchronization burst sequence (Sync Code) for each individual signal, and provides a code tracking delay-lock loop for achieving accurate timing of each individual signal.
The novelty of this invention is the use of special Sync Code sequences in the otherwise well known Time-Gated Delay Lock Loop (Spilker,J. J.,"Digital Communications by Satellite," Englewood Cliffs, N.J. 1977, Prentice-Hall, pp 555-569). These Sync Codes are specified so that the interference between Return Link signals which are coincident in time and frequency is minimized, which means that the code tracking and synchronization process for each signal is relatively unaffected by others. In a DOCDMA communications system, the subscribers on odd carriers (f.sub.1, f.sub.3,f.sub.5 . . . ) are assigned one-half the total set of Sync Codes available, and the subscribers on even carriers (f.sub.2, f.sub.4, f.sub.6 . . . ) are assigned the other half. To implement the code tracking loop, a portion of the Forward Link information capacity is allocated to the signal timing error data which the remote station uses for timing correction. It is assumed that each remote station receives its own timing error data in a robust, uncorrupted manner. A portion of the Return Link information capacity is allocated to the Sync Code which is received by the hub station and processed by the Delay Discriminator. This code tracking loop as described is shown in FIG. 3.
The Sync Codes are specified in sets and possess special properties which provide the desirable characteristics of minimal interference when all of the codes are nearly coincident. The Sync Codes are constructed using a basis sequence of length N, b.sub.0, b.sub.1, . . . ,b.sub.n-1, with each element in the basis sequence drawn from a binary alphabet {-1, +1}. This basic sequence has a two valued circular auto-correlation function, which is given as ##EQU1##
The Sync Code sequences are constructed as follows.
1) The number of symbols in a Sync Code sequence is N+5.
2) Denoting the symbols of the k.sup.th Sync Code sequence as a.sub.o (k), a.sub.1 (k), a.sub.2 (k), . . . , a.sub.N+4 (k), then the first 3 symbols are fixed such that a.sub.o (k)=+1, a.sub.1 (k)+1, and a.sub.2 (k)=+1.
3) The fourth symbol of the Sync Code is the same as the symbol previous to the last such that a.sub.3 (k)=a.sub.N+3 (k), where a.sub.N+3 (k) is determined in Step 4.
4) The next N symbols of the Sync Code, a.sub.4 (k), a.sub.5 (k), . . . , a.sub.N+3 (k), are obtained from a circular shift of the basis sequence such that a.sub.i (k)=b.sub.(i+J(k))mod(N) for i=4, 5,. . . ,N+3 and for a given J(k), 0.ltoreq.J(k).ltoreq.N-1. The set J consists of the circular shift indices for the K remote stations. The definition of the values in the set J is crucial to the functionality of this invention. To a large degree it is the proper selection of the circular shift indices that provides for minimal interference between the Return Link Sync Codes. Since the use of a Sync Code sequence is in conjunction with a Delay Discriminator, the operational limitations of the discriminator will dictate the design. As will be described next, this limitation leads to the following rule for selecting the circular shift indices in J.
Rule: The set J consisting of the circular shift indices is divided into 2 subsets J.sub.odd and J.sub.even corresponding to the odd numbered carriers and even numbered carriers, respectively. The minimum difference between all pairs of indices in either subset must be greater than one, that is: ##EQU2##
5) The last symbol of the Sync Code is the same as the fifth symbol such that a.sub.N+4 (k)=a.sub.4 (k) where a.sub.4 (k) is determined in Step 4.
There are several types of binary sequences that may be used as the basis sequence, which have the preferred two valued auto-correlation function. If N+1 is a power of 2, then one of the most obvious choices is the m-sequence or maximal length shift register sequence (Golomb, Solomon W., "Shift Register Sequences, Revised Edition," Laguna Hills, Calif., 1982, AEGEAN PARK PRESS). In the event that N+1 is not a power of 2, then an m-sequence cannot be used as a basis sequence without modification. Other sequences which have the preferred two valued auto-correlation function but do not in general have length of the form 2.sup.n -1 can be used as basis sequences. Such sequences include Legendre (Quadratic Residue) sequences and Twin Prime sequences, for example. Since the number of Sync Codes required by a multiple access communications system may be less than the number of elements in J, then any subset of J can be used.